20121109

Physics quiz question: Caliente Mountain air pressure

Physics 205A Quiz 5, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 9.19(b)

Caliente Mountain from Fox Mountain.
"Caliente Mountain from Fox Mountain"
David Stillman
flic.kr/p/dUAprv

The summit of Caliente Mountain (1,556 m above sea level), near New Cuyama, is the highest point in San Luis Obispo county[*]. Assume that the variation of gravitational constant g and the density of air ρair = 1.2 kg/m3 with elevation is negligible. (Patm = 101.3 kPa.) The air pressure at the summit is:
(A) 1.8×104 Pa.
(B) 8.3×104 Pa.
(C) 1.2×105 Pa.
(D) 1.5×106 Pa.

[*] wki.pe/Caliente_Mountain.

Correct answer (highlight to unhide): (B)

For static fluids, the energy density relation between pressure and changes in elevation is given by:

0 = ∆P + ρ·g·∆y,

0 = (PCalientePsea level) + ρ·g·(yCalienteysea level),

where the air pressure at sea level is 101.3 kPa = 1.013×105 Pa, such that:

PCaliente = Psea level – ρ·g·(yCalienteysea level),

PCaliente = 1.013×105 Pa – (1.2 kg/m3)·(9.80 m/s2)·(1,556 m – 0 m),

PCaliente = 1.013×105 Pa – 0.18×105 Pa = 0.83×105 Pa = 8.3×104 Pa.

(Response (A) is ρ·g·∆y, which is the relative pressure decrease between sea level and Caliente Mountain; response (C) is Psea level + ρ·g·∆y; response (D) is (1/2)·ρ·(∆y)2.)

Sections 70854, 70855
Exam code: quiz05L4mN
(A) : 24 students
(B) : 15 students
(C) : 3 students
(D) : 10 students

Success level: 29%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.39

No comments: